False dilemma

False dilemma, also called the either-or fallacy and the fallacy of false choice, is a mistake in logic that allows only two possibilities when more exist.

For example, there is "either-or fallacy" in saying that an apple must be green or red. The premise is that the apple is either one color or another; but this beginning is a mistake because some apples—not most—are other colors. In other words, most apples are red or green, but some are also yellow.

A "fallacy of false choice" may hide a deliberate attempt to eliminate agreement on an issue. Eldridge Cleaver used this tactic when he said: "You're either part of the solution or part of the problem."[1]

A false dilemma may also be used for comedic effect. Stephen Colbert used this tactic when he asked guests on The Colbert Report: "George Bush... great president or the greatest president?"